This answer comes from the perspective of a manager with experience of at least 30 direct reports and up to 250 indirect reports dealing with ADA, PDA and FMLA issues almost on a weekly basis. It is meant to address not only the OP but the many numerous incorrect interpretations of employment law/policies posted here.
Note: Do not construe this answer as what my personal thoughts are on this, but rather a pragmatic analysis of the employee's position as it relates to the question.
In this situation, what should she do? I can't see how she could be
forced outside for this but maybe I'm wrong. My first concern is for
my wife and our unborn child.
There's nothing she can do.
Why? Let's have a look.....
ADA doesn't cover pregnancies
This one is a simple case; the ADA doesn't consider pregnancy a disability or a substantial impairment. The definition of a disability can be found in Title 42, Chapter 126, § 12102 of the US Code.
PDA has to do with discrimination as it relates to employment
The Pregnancy Disability Act basically adds pregnancy and pregnancy related medical conditions to the Civil Rights Act of 1964. Basically you cannot treat pregnant women any differently you would anyone else, just as you cannot treat people of different races or religions any differently. A simple, but succinct way to look at this is "What you offer to one, you offer to all."
FMLA is related to leave
It's the Family and Medical Leave Act.
The FMLA entitles eligible employees of covered employers to take
unpaid, job-protected leave for specified family and medical reasons
with continuation of group health insurance coverage under the same
terms and conditions as if the employee had not taken leave.
Pregnancy IS covered here. However, it has to do with leave, not accommodations. It gives you up to 12 weeks of guaranteed, non-contiguous leave (day-to-day as needed), unpaid leave to deal with pregnancy.
In other words, under FMLA, you can take a day (unpaid) as needed anytime you are pregnant provided you have submitted the notice to your employer without loss of your employment or benefits. FMLA doesn't cover job modification.
It's also important to note that *An employee on FMLA leave is not protected from actions that would have affected him or her if the
employee was not on FMLA leave.
Third Trimester is NOT an impairment
Medically speaking, there's no evidence that a pregnant woman is anyhow impaired, impeded or unable to perform their job functions.
Generally speaking, there's no medical reason for not being able to do normal activities including standing, walking, and being outside. The symptoms associated with pregnancy are treated with over-the-counter remedies including, but not limited to acetaminophen, extra water for hydration, and sunscreen.
Under a number of laws, employers are required to make reasonable accommodations to the employee; obviously, going inside and switching out positions with another staff member appears to be a zero-cost accommodation.
However, while an employer is barred from asking why an employee needs an accommodation, and employee cannot merely state they need one and expect it to be granted. A "doctors note" will only describe the accommodation, not the medical condition that caused it.
OSHA classifies this as "Lower Risk Level"
The Occupational Safety and Health Administration classifies this in a lower risk category and advises caution. They even provide an action plan for this and each of the stages.
I'm not saying it's impossible for a pregnant woman to become ill working in 90° weather, I'm saying that making the argument that she needs an accommodation because she might get ill is speculation. In other words, this is considered low risk and to grant an accommodation will require documentation (i.e. a doctors note).
TL; DR: Summary
There's no legal requirement to make a workplace accommodation for pregnancy with the exception that it being documented with a "doctors note" specifying the limitations and/or work restrictions
She was entitled to medical leave, but she didn't take it (nor is it known that FMLA paperwork was filed)
She may have had sick days accrued, but chose not to use them. In my experience, teachers typically are responsible for arranging their own substitutes (directly or via dept. head). This was also not indicated that it was done.
Large employers (school districts fall under this) have rules and procedures often negotiated with the relevant union (teachers, in this case). If an accommodation is required, the employee must supply documentation of the need.
(IMO) The principal is adhering to the rules re: asking for an accommodation. Allowing her to change her schedule without proper documentation sets a precedent that anyone can obtain an accommodation by simply asking.
Now, if someone else makes a request and the principal doesn't grant it, he and the school (district) are in hot water for showing favoritism (which is a violation of union contracts).
Bottom line: You're looking for an exemption where there isn't one and you're looking for an accommodation without going through the proper procedure.